Another method is to ask the event facilitator ahead of time to get ideas from the audience as to issues they might want you to discuss. This way you'll be addressing concerns specific to the audience.

A slightly more complex approach is taking a generally accepted issue, proposing a contrary view and presenting alternative viewpoints.

For example, 'beer is healthy for you' or that 'animal-derived clothing textiles are better for the environment than synthetics'. This can only be pulled off if you are very well versed in the matter, have strong supporting evidence and fairly good speaking skills because you'll be a minority in the face of a majority audience with opposing opinions.

Whatever method you use to select your problem topic ensure that you have clear examples, convincing facts or credible data that supports your position on the matter.

When discussing several problems in one speech, organize your speech such that you present a solution after each problem you mention. This way the audience follows your argument well and doesn't get muddled about which answer is for what problem.

Problem solution speech topics can also include the causes of the problem before you give the solutions. Identifying the underlying causes help support your explanation and gives your solution more credibility.

Additionally, your personal opinion on the matter should be in line with the solutions you are presenting because your passion for the topic will come through in the delivery.

If you have bought into the solution, then your speech will be more persuasive and you will be in a better position to swing the audience to your viewpoint.

At the conclusion of the speech, summarize the issues, especially the solutions, as this is what you want your audience to remember best.

If you are having to work on problem solution speech topics in a classroom environment then you were probably given the subject you are to talk on. Keep everything above in mind when you write your speech up and you'll do great!